GATE CS 2015 Set 1 — Question 39
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Computer Networks → Medium Access & LANs → ALOHA (Pure, Slotted)
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Question
Consider a LAN with four nodes and . Time is divided into fixed-size slots, and a node can begin its transmission only at the beginning of a slot. A collision is said to have occurred if more than one node transmit in the same slot. The probabilities of generation of a frame in a time slot by and are 0.1, 0.2, 0.3 and 0.4, respectively. The probability of sending a frame in the first slot without any collision by any of these four stations is ________.
Correct answer
0.4 to 0.46
Solution
Let be the probability that station generates a frame in a time slot.
Given:
Let be the probability that station does NOT generate a frame in a time slot.
For a frame to be sent in the first slot without any collision, exactly one station must transmit, and the other three must not transmit. We assume the events of each station transmitting are independent.There are four mutually exclusive scenarios for a successful transmission:
The total probability of sending a frame in the first slot without any collision is the sum of these probabilities:
Total Probability
Total Probability The probability is 0.4404.
Given:
Let be the probability that station does NOT generate a frame in a time slot.
For a frame to be sent in the first slot without any collision, exactly one station must transmit, and the other three must not transmit. We assume the events of each station transmitting are independent.There are four mutually exclusive scenarios for a successful transmission:
1.Only transmits:
2.Only transmits:
3.Only transmits:
4.Only transmits:
The total probability of sending a frame in the first slot without any collision is the sum of these probabilities:
Total Probability
Total Probability The probability is 0.4404.
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